 {x|-3 ≤ x ≤ 16, x ∈ ℤ}

 Describe the set of numbers using set- builder notation. {8, 9, 10, 11, 12, …}  The set of numbers is always considered x unless otherwise stated  So we start with: {x| ◦ This means “the set of number x such that…”

 Describe the set of numbers using set- builder notation. {8, 9, 10, 11, 12, …}  This set only has numbers starting at 8 and increasing  We write that as an inequality: x ≥ 8  This includes all the numbers in the set!  At this point we have: {x| x ≥ 8

 Describe the set of numbers using set- builder notation. {8, 9, 10, 11, 12, …}  We now have to state what set of number x is an element of  Since these numbers are positive whole numbers, the set is W ◦ We can write this as x ∈ W

 Describe the set of numbers using set- builder notation. {8, 9, 10, 11, 12, …}  We can then put everything together for the final answer: {x| x ≥ 8, x ∈ W}  Verbally this reads: The set of all x such that x is greater than or equal to 8 and x is an element of the set of whole numbers

 Example 2: Write the following in set-builder notation: x < 7  There’s no stipulation on the numbers as long as they’re less than 7, so it can be all real numbers  Therefore: {x| x < 7, x ∈ ℝ}

 Example 3: All multiples of 3  In this case, x is equal to 3 times any number ◦ We write this as x = 3n  In this case, multiples of 3 can only be an integer (positive or negative whole numbers or zero)  {x| x = 3n, x ∈ ℤ}

1. {1, 2, 3, 4, 5, …} 2. x ≤ < x ≤ All multiple of ∏